1. The problem is to understand the logarithm function and how to work with it. 2. The logarithm function is defined as the inverse of the exponential function. For a base $b > 0$, $b \neq 1$, the logarithm of a number $x$ is written as $\log_b(x)$ and satisfies the equation: $$b^{\log_b(x)} = x$$ 3. Important rules for logarithms include: - Product rule: $\log_b(xy) = \log_b(x) + \log_b(y)$ - Quotient rule: $\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)$ - Power rule: $\log_b(x^r) = r \log_b(x)$ - Change of base formula: $\log_b(x) = \frac{\log_k(x)}{\log_k(b)}$ for any positive $k \neq 1$ 4. To solve logarithmic problems, apply these rules step-by-step, simplify expressions, and convert between exponential and logarithmic forms as needed. This explanation covers the basics of logarithms and their properties to help you understand and solve logarithmic problems.